J Therm Anal Calorim DOI 10.1007/s10973-016-5319-8
Thermodynamic investigation of Rb2FeTi(PO4)3 phosphate of langbeinite structure V. I. Pet’kov1 • E. A. Asabina1 • A. V. Markin1 • A. A. Alekseev1 • N. N. Smirnova1
Received: 11 November 2015 / Accepted: 2 February 2016 Akade´miai Kiado´, Budapest, Hungary 2016
Abstract The temperature dependence of molar heat capacity for Rb2FeTi(PO4)3 phosphate was investigated between T = 6 and 650 K by precision adiabatic vacuum and differential scanning calorimetry in this research. The anomaly was observed in the heat capacity curve, and its character was explained by magnetic disorder–order phase transition at T below 6 K. The standard thermodynamic o functions Cp;m ; Hmo ðTÞ Hmo ð6Þ ; Som ðTÞ Som ð6Þ ; Uom of Rb2FeTi(PO4)3 within the range T ? 6–650 K were calculated. The low-temperature heat capacity analysis, performed based on the Debye theory and multifractal model, leads to the conclusion of framework structural topology of the studied phosphate. Keywords Thermodynamic properties Rb2FeTi(PO4)3 phosphate Adiabatic calorimetry DSC Heat capacity Fractal dimension
Introduction Many sulfates, phosphates, silicates, molybdates and other salts crystallize in the langbeinite (K2Mg2(SO4)3, cubic system, space group P213 [1]) structural type [2–6]. The substances are characterized by the framework structure. The langbeinite-type phosphates family may be described by (M1)[9] (M2)[6–12] [(L1)[6] (L2)[6] (PO4)3]3? crystalchemical formula. The L sites with octahedral oxygen coordination are usually occupied by cations in oxidation state ?2, ?3 and ?4, and their ionic radii vary from 0.5 to
& E. A. Asabina
[email protected] 1
Lobachevsky State University of Nizhni Novgorod, Prospekt Gagarina 23, 603950 Nizhni Novgorod, Russian Federation
˚ . LO6 octahedra are connected together with PO4 1A tetrahedra. Large closed structural cavities are available to be occupied by cations in oxidation states ?1 and ?2, their ˚ , and coordination number is 9 ionic radii are more than 1 A in ideal structure (in some cases, coordination numbers from 6 to 12 are realized). The present study is the beginning of thermophysical properties investigation of langbeinite structure phosphates, which are of interest as ferroelastic and luminescent materials, perspective ecologically safe crystal forms for nuclear wastes solidification [4, 7]. The immobilization in ceramic materials for an underground repository can be considered one of the options for the management of long-lived and highly active radionuclides [8]. At the present time, only phosphate glasses [9–12] and several ceramic phosphate materials [13–17] were thermodynamically studied for this purpose. Any information concerning the thermodynamic description of langbeinite-type phosphates is absent. In this work, temperature dependence of the Rb2FeTi(PO4)3 phosphate heat capacity was studied calorimetrio cally between T = 6 and 650 K. The Cp;m ¼ f ðT Þ character was explained. The standard thermodynamic functions, namely heat capacities, enthalpies, entropies and Gibbs energy of Rb2FeTi(PO4)3 within the range T ? 6–650 K, were calculated. The type of the phosphate structural topology was confirmed using multifractal model for the low-temperature 30–50 K heat capacity data processing.
Experimental Sample The Rb2FeTi(PO4)3 phosphate was synthesized by solidstate reactions according to the following summary equation:
123
V. I. Pet’kov et al.
4RbCl þ 2TiO2 þ Fe2 O3 þ 6NH4 H2 PO4 ! 2Rb2 FeTiðPO4 Þ3 þ6NH3 þ 4HCl þ 7H2 O
ð1Þ
The following reactants (REACHEM [18]) were used as the initial compounds: rubidium chloride RbCl (the mass fraction of the main component was 0.99), finely dispersed titanium oxide TiO2 in the anatase modification (0.999), iron oxide Fe2O3 in the haematite modification (0.99) and ammonia dihydrogen phosphate NH4H2PO4 (0.995). The reactants, taken in stoichiometric amounts, were carefully mixed in an agate mortar (on the basis of 40 min of grinding per gram of the initial mixture). Fine mixture of reagents was dried at 473 K for 12 h and then thermally treated in corundum crucible at 873, 1073 and 1173 K for 24–30 h at each stage of atmospheric pressure in air. Thermal treatment stages were alternated with careful grinding. Treatment at 1273 K was used for obtaining the sample of high crystallinity. The synthesized sample is a white-colored polycrystalline powder. Its characterization was provided by electron microscopy, microprobe analysis, X-ray diffraction and IR-spectroscopy. The results are previously reported in [19]. Chemical composition and homogeneity of the sample were confirmed using a CamScan MV-2300 (VEGA TS 5130MM) electron microscope equipped with YAG detectors of backscattered and reflected electrons and energy-dispersive X-ray microanalyzer with semiconductor Si(Li) detector Link INCA ENERGY 200C. The results showed that the studied sample consists of grains of sizes from 1 to 20 lm (Fig. 1). The microprobe analysis data confirmed that the sample is homogeneous and its composition Rb1.99(8)Fe1.00(2)Ti0.99(6)P3.00(1)O12 corresponds to the theoretic one within the uncertainty of determination. No significant impurities were found within the detection limit. The X-ray powder diffraction pattern of Rb2FeTi(PO4)3 was obtained at room temperature on a STOE STADI MP
diffractometer with a linear position-sensitive detector (CuKa1 radiation, asymmetric Ge(111) monochromator, transmission geometry). The data were recorded using the 2h scan mode from 15.00 to 80.50 at a step of 0.02. Taking into account that the X-ray pattern of the sample (Fig. 2a) contains only sharp diffraction peaks without asymmetry and also the absence of significant noise and amorphous diffuse halo, we may conclude that the studied phosphate is totally crystalline. X-ray results confirmed phase purity of the studied phosphate and its crystallization in the langbeinite structural type with cubic symmetry (space group P213, Z = 4) [1–6, 19]. The unit cell ˚, parameters of the studied compound are: a = 9.8892(2) A 3 ˚ V = 967.12(1) A . The results of Rietveld refinement [19] show that Rb2FeTi(PO4)3 crystal structure bases on framework are formed by corner-sharing (Fe/Ti)O6 octahedra and PO4 tetrahedra (Fig. 2b). The main structural elements of the framework are fragments, consisting of two octahedra and three tetrahedra. Such fragments form columns, oriented in four directions, parallel to the cube diagonals. Rb? cations completely occupy two nine-coordinated sites in large ellipsoidal cavities between the columns of the polyhedra of the langbeinite framework. Functional composition of Rb2FeTi(PO4)3 was confirmed by IR-spectroscopy using a Specord 75IR spectrophotometer in the wavenumber range from 1400 to 400 cm-1. The sample was prepared for investigation as a fine-dispersed film on KBr substrate. The results showed the absence of amorphous impurities (for example, pyrophosphates) in the studied sample. The absorption bands form and location in the obtained IR-spectrum (Fig. 3) are typical for the langbeinite-type orthophosphates with the space group P213 [20, 21]. From the complex of analyses results, the sample under consideration contains not less than 0.98 mass fraction of the main substance (Table 1). These impurities were not identified; however, B2 9 10-2 of their mass fraction was irrelevant to the accuracy of the thermodynamic data. Apparatus and measurement procedure
Fig. 1 Electron microscope image of Rb2FeTi(PO4)3
123
A BCT precision automatic adiabatic calorimeter (Termis, Moscow) was used to measure isobaric heat capacities o (Cp;m ) of Rb2FeTi(PO4)3 over the temperature range of 6–345 K. The design and operation of the calorimeter were described in detail earlier [22, 23]. The relative uncertainty o in heat capacity measurements was 2 9 10-3 Cp;m over the o main temperature range of 40–345 K, 5 9 10-3 Cp;m o between T = 15–40 K and within 2 9 10-2 Cp;m at T \ 15 K. The accuracy of the calorimeter was verified using standard reference samples (benzoic acid and a-Al2O3).
Thermodynamic investigation of Rb2FeTi(PO4)3 phosphate of langbeinite structure
(b)
(a)
12
c
Intensity × 10–3/pulse
10 a
8
b
6 PO4 4
(Fe/Ti)O6 Rb
2
0
1, 2 3 4 40
20
60
2θ /°
455
1025 990 945
1120
550
Transmittance/a.u.
642 585
Fig. 2 a X-ray diffraction patterns of Rb2FeTi(PO4)3: 1 observed, 2 calculated, 3 Bragg reflections, 4 difference; b crystal structure of Rb2FeTi(PO4)3
1200
400
800
− ν/cm–1
Fig. 3 IR-spectrum of Rb2FeTi(PO4)3
A titanium calorimetric cell with a volume of 1.5 cm3 was loaded with a sample and then degassed in vacuum with a residual pressure of &5 Pa. Dry helium gas (at p = 4 kPa and room temperature) was introduced into the cell to facilitate heat transfer during the measurements. The sample mass used for calorimetric measurements was 0.5738 g. An iron–rhodium resistance thermometer placed on the inner surface of the adiabatic shield was used for the temperature measurements in the calorimetric experiments. The temperature difference between the cell and the shield
was determined by a differential copper–iron–chromel thermocouple. The sensitivity of the thermometric circuit was 10-3 K. After assembling, the measuring system was cooled in a liquid nitrogen bath. If the measurements were performed below 80 K, a liquid helium bath was used. The sample was cooled to the temperature of the measurement onset at a rate of 10-2 K s-1. Then, the sample was heated with a temperature step of 0.5–2 K at a rate of 10-2 K s-1. Sample temperature was recorded after an equilibration period (temperature drift \10-2 K s-1, approximately 10 min per experimental point). The ratio of the sample heat capacity to the total (sample ? cell) one was from 0.4 to 0.7. Heat capacity of Rb2FeTi(PO4)3 over the range of 330– 650 K was measured in a DSC 204 F1 Phoenix differential scanning calorimeter (Netzsch Gera¨tebau, Germany) with use of l-sensor. The calorimeter was calibrated and tested against melting of n-heptane, adamantane, indium, tin, bismuth and zinc. The heat capacity was determined by the ‘‘ratio method’’, with sapphire used as a standard reference sample. The techo nique for determining Cp;m according to the data of DSC measurements is described in detail in a Netzsch Software Proteus and in [24, 25]. The relative standard uncertainty o for heat capacities was 2 9 10-2 Cp;m . Measurements were carried out in argon atmosphere. Liquid nitrogen was used as a cryogen.
Table 1 Sample information Formula
Sources
State
Mass fraction purity
Analysis method
Rb2FeTi(PO4)3
Present work, [19]
powder
0.98
Electron microprobe analysis, X-ray diffraction, IR-spectroscopy
123
V. I. Pet’kov et al.
Results and discussion
Table 2 Experimental molar heat capacity Cp,m of crystalline Rb2FeTi(PO4)3 from adiabatic calorimetry, M = 559.5617 g mol-1
Molar heat capacity
T/K
Experimental heat capacity data for Rb2FeTi(PO4)3 in the temperature range of 6–650 K are plotted in Fig. 4 and given in Tables 2, 3. Heat capacity of the sample rises gradually with temperature increase over the main temperature interval. At the same time, heat capacity of the studied compound was found to increase with temperature decrease in the range of 6.2–10.2 K (inset in Fig. 4). o The experimental points of Cp;m were fitted using least squares method in the temperature range of 20–650 K, and the polynomial equation of the temperature dependency of o Cp;m was the following: i k X T o ¼ ai ln ; ð2Þ Cp;m 30 i¼0
Series 1
Heat capacity/J mol–1 k–1
where ai are polynomial coefficients and k is polynomial degree. The relative standard uncertainty for the heat o capacities was 5 9 10-3 Cp;m in the temperature range of -3 o 20–90 K, 2.5 9 10 Cp;m between T = 80–350 K and -3 o 6 9 10 Cp;m between T = 350 to 650 K. The low-temperature heat capacity of Rb2FeTi(PO4)3 is found not to obey the Debye’s theory. Such anomaly observed in the heat capacity curve is likely to be descending branch for magnetic disorder–order phase transition, which lies outside the measuring range of the calorimeter. Such anomalies have not yet been studied for the langbeinite-like phosphates family, because of lack of their calorimetric data, but they are well known for other
6.37
6.63
6.35
6.87
6.34
7.07
6.31
7.27 7.48
6.30 6.27
7.70
6.24
7.91
6.20
8.14
6.17
8.31
6.14
8.61
6.09
8.85
6.06
9.14
6.01
9.37
5.99
9.65
5.95
9.94
5.93
10.25
5.92
10.58
5.93
10.94
5.95
11.33 11.73
5.98 6.02
12.24
6.09
12.92
6.18
13.79
6.36
14.66
6.61
15.55
7.00
16.54
7.66
17.61
8.51 9.51 10.58
22.35
13.52
25.07
17.17
27.68
21.94
30.29
27.04
20
32.93
32.50
10
35.56 38.13
38.21 43.22
40.71
48.52
43.27
53.65
45.83
58.48
48.23
63.75
48.39
63.87
50.57
68.81
53.10
73.70
55.64
78.96
58.18
83.31
0
400
10
20
600
Temperature/K o Fig. 4 Experimental molar heat capacity Cp;m of Rb2FeTi(PO4)3 as a function of temperature: Results of adiabatic calorimetry are given by open circle symbol; results of differential scanning calorimetry are given by filled circle
123
6.39
6.43
19.80
200
200
6.26
18.69
400
0
Cp,m/J mol-1 K-1
Thermodynamic investigation of Rb2FeTi(PO4)3 phosphate of langbeinite structure Table 2 continued T/K
Table 2 continued -1
Cp,m/J mol
-1
K
T/K
Cp,m/J mol-1 K-1
60.74
87.29
127.48
181.6
63.29
91.16
130.52
185.3
65.84
95.07
133.56
188.9
99.08
68.33
136.59
192.5
70.80
102.8
139.61
196.4
73.33
106.4
142.62
199.3
75.86
110.1
145.63
202.9
78.10 78.39
113.1 114.2
148.64 151.64
206.5 210.0
80.91
117.4
154.65
213.1
81.44
117.8
157.65
216.7
84.54
122.8
160.64
219.9
87.63
127.0
163.63
223.0
Series 2
166.61
225.7
6.54
6.36
169.59
228.7
6.76
6.34
172.57
231.7
6.97
6.33
175.56
234.3
7.17
6.31
178.53
237.1
7.41
6.29
181.49
239.8
7.58
6.26
184.44
242.4
7.74
6.23
187.39
244.9
7.82
6.21
190.34
247.5
8.06 8.21
6.18 6.15
193.00 196.22
249.8 252.4
8.42
6.12
199.15
254.8
8.54
6.10
202.07
257.2
8.72
6.07
205.00
259.8
8.91
6.04
207.93
261.9
9.03
6.03
210.87
264.1
9.26
6.00
213.82
266.2
9.55
6.00
216.76
268.4
9.79
5.94
219.70
270.4
10.08
5.92
222.66
272.4
225.61
274.6
Series 3 83.42
121.0
228.57
276.6
85.94
124.4
231.52
278.4
90.71
130.8
234.60
280.4
93.77
135.6
237.44
282.2
96.86 99.95
140.0 144.5
240.40 243.37
283.9 285.7
103.01
148.9
246.32
287.3
106.07
153.6
249.25
289.0
109.14
157.5
252.17
290.5
112.20
161.3
255.08
292.4
115.26
166.0
257.97
293.9
118.31
170.1
260.85
295.7
121.37
174.0
263.71
297.2
124.41
177.5
266.54
298.9
123
V. I. Pet’kov et al. Table 2 continued -1
-1
So, the studied compound probably will show peak at o ¼ f ðT Þ dependence, which is origiT \ 6 K on the Cp;m nated from magnetic transition. As heat capacity of Rb2FeTi(PO4)3 does not exhibit any peculiarities at T [ 10.2 K, the value of the fractal dimension D—the important parameter of the multifractal model of lowtemperature heat capacity treatment [29, 30]—was estimated from our experimental data. In this model, the exponent of T in the equation for isochoric heat capacity is referred to as fractal dimension (D). The D value allows one to indicate on the structure topology. The calculation method of D is described in [30]. The basic equation of the multifractal model was given as follows:
T/K
Cp,m/J mol
269.33
300.4
272.13
302.1
274.91
303.5
277.67
305.1
280.41
306.7
283.13
308.2
285.83
309.7
288.50 291.15
311.0 312.5
293.78
314.1
296.39
315.4
298.97
316.8
301.53
318.2
304.07
319.8
306.61
320.9
309.09
322.4
311.37
323.6
313.85
325.1
316.30
326.4
318.72
327.7
321.07
329.0
323.37
330.0
325.72 328.06
332.0 332.8
Thermodynamic functions
330.41
334.2
332.76
335.3
335.11
336.1
337.46
337.6
339.81
338.6
342.16
340.2
344.50
341.7
As stated above, the extrapolation of heat capacity down to T = 0 K was not performed. For this reason, we cannot assume the residual entropy to be zero. Hence, the standard thermodynamic functions were calculated from 6 K. The calculations of enthalpies Hmo ðTÞ Hmo ð6Þ and o entropies Sm ðTÞ Som ð6Þ were made by the integration of o o ¼ f ðT Þ and Cp;m ¼ ln f ðT Þ curves, respectively. The Cp;m o Gibbs energies Um over the studied temperature range were determined with (4): Uom ¼ Hmo ðTÞ Hmo ð6Þ Som ðTÞ Som ð6Þ ð4Þ
K
The standard uncertainty for temperature u(T) = 0.01 K in the temperature range from T = 6–345 K. The relative standard uncertainty for heat capacity ur(Cp,m) = 0.02 in the temperature range from T = 6–15 K, ur(Cp,m) = 0.005 between T = 15–40 K, ur(Cp,m) = 0.002 in the temperature range from T = 40–345 K
classes of substances (for example, [22, 26–28]). In general, low-temperature anomalies in heat capacity for a magnetically ordered material may be attributed either to the electronic Schottky anomaly or a transition to magnetically ordered state. In order to give the quantitative description for phase transitions under consideration, magnetic susceptibility measurements as well as heat capacity determined in an external magnetic field are required.
123
o Cv;m ¼ 3DðD þ 1ÞkNcðD þ 1ÞnðD þ 1ÞðT=Hmax Þ;
ð3Þ
where N is the number of particles, k is the Boltzmann constant, c(D ? 1) is the Gamma function, n(D ? 1) is the Riemann function, and Hmax is the characteristic temperature. o o By calculations, it was stated that Cp;m is equal to Cv;m at T \ 50 K. We found D = 3 and Hmax ¼ 218 K for Rb2FeTi(PO4)3 in the range from 30 to 50 K. The obtained fractal dimension value is in good agreement with the data on its framework (three-dimensional) topology of structure.
The calculation procedure was described in detail elsewhere [31, 32]. The obtained functions of crystalline Rb2FeTi(PO4)3 in the interval from 6 to 650 K are listed in o Table 4. It is seen that the Cp;m values at high temperatures become close to the theoretically estimated ones from P. Dulong and A. Petit rule: o Cp;m ¼ 3Rn;
ð5Þ
where R = 8.3144621 J mol-1 K-1 and n is number of atoms in the formula unit. The calculated theoretical molar heat capacity of Rb2FeTi(PO4)3 at high-temperature was *474 J mol-1 K-1, which coincides with the experimental data within the uncertainty of determination.
Thermodynamic investigation of Rb2FeTi(PO4)3 phosphate of langbeinite structure Table 3 Experimental molar heat capacity Cp,m of crystalline Rb2FeTi(PO4)3 from differential scanning calorimetry, M = 559.5617 g mol-1 T/K
Cp,m/J mol-1 K-1
T/K
Cp,m/J mol-1 K-1
T/K
Cp,m/J mol-1 K-1
333.9
335
443.8
394
553.1
445
340.0
339
449.2
396
558.4
449
345.9
342
454.5
399
563.7
450
351.7
345
459.8
403
569.0
454
357.3
347
465.2
405
574.3
454
362.7
350
470.6
408
579.7
457
368.0
353
476.0
410
585.1
459
373.3
355
481.4
414
590.6
461
378.6
359
486.9
417
596.0
463
383.9
361
492.5
419
601.4
465
389.3 394.8
364 368
498.0 503.5
420 424
606.8 612.2
467 468
400.3
371
509.1
426
617.8
470
405.8
374
514.7
427
623.3
472
410.4
376
520.3
430
628.8
473
416.0
379
525.8
433
634.2
475
421.7
384
531.2
436
639.5
476
427.3
385
536.7
438
644.9
477
432.9
389
542.2
442
650.3
479
438.4
392
547.7
445
The standard uncertainty for temperature u(T) = 0.5 K in the interval between T = 330 and 650 K. The relative standard uncertainty for heat capacity ur(Cp,m) = 0.02 over the range from T = 330–650 K
o Table 4 Thermodynamic functions of crystalline Rb2FeTi(PO4)3, M = 559.5617 g mol-1; Cp;m , molar heat capacity; Hmo ðTÞ Hmo ð6Þ , molar o enthalpy; Sm ðTÞ Som ð6Þ , molar entropy; Uom ¼ Hmo ðTÞ Hmo ð6Þ Som ðTÞ Som ð6Þ at the pressure p = 0.1 MPa o o o T/K Cp;m /J mol-1 K-1 Uom /kJ mol-1 Hm ðTÞ Hmo ð6Þ /kJ mol-1 Sm ðTÞ Som ð6Þ /J mol-1 K-1 6
6.45
0
0
0
10
5.92
0.0246
3.15
0.00694
15
6.73
0.0609
5.59
0.0229
20
10.77
0.09730
8.026
0.06327
25
17.06
0.1852
11.49
0.1020
30
26.51
0.2731
14.95
0.1753
35
36.91
0.4575
20.18
0.2488
40
47.05
0.6418
25.41
0.3746
45
57.05
0.9273
31.74
0.5009
50 60
67.33 86.40
1.213 2.070
38.07 52.33
0.6906 1.069
70
101.5
2.927
66.59
1.734
80
116.0
4.087
81.09
2.400
90
130.3
5.247
95.58
3.355
100
144.6
6.693
110.0
4.311
110
158.6
8.138
124.5
5.556
120
172.1
9.858
138.8
6.802
130
184.7
11.58
153.2
8.334
140
196.4
13.54
167.2
9.866
123
V. I. Pet’kov et al. Table 4 continued
Hmo ðTÞ Hmo ð6Þ /kJ mol-1
Som ðTÞ Som ð6Þ /J mol-1 K-1
T/K
o Cp;m /J mol-1 K-1
150
208.1
15.51
181.2
11.68
160
219.1
17.69
194.9
13.49
170
229.1
19.88
208.6
15.58
180
238.4
22.27
221.8
17.67
190
247.2
24.65
235.1
20.02
200 210
255.6 263.4
27.21 29.76
247.9 260.7
22.37 24.98
220
270.7
32.47
273.0
27.58
230
277.5
35.17
285.3
30.44
240
283.7
38.01
297.1
33.29
250
289.4
40.84
308.9
36.38
260
295.1
43.80
320.3
39.47
270
300.8
46.75
331.6
42.79
280
306.4
49.78
342.6
46.16
290
311.9
52.90
353.4
49.59
298.15
316.4
55.44
362.2
52.56
300
317.4
56.03
364.1
53.22
310
322.9
59.22
374.7
56.92
320
328.5
62.51
384.9
60.67
330
333.6
65.79
395.2
64.62
340
338.8
69.18
405.2
68.57
350 360
344.3 349
72.57 76.1
415.1 425
72.72 76.9
370
354
79.5
435
81.2
380
359
83.1
444
85.6
390
365
86.7
453
90.1
400
370
90.4
463
94.6
410
376
94.1
472
99.4
420
382
97.9
481
104
430
387
102
490
109
440
392
106
499
114
450
397
110
508
119
460
402
114
517
124
470
407
118
525
129
480
412
122
534
135
490
417
126
543
140
500 510
421 426
130 134
551 559
145 151
520
431
139
568
157
530
435
143
576
162
540
440
147
584
168
550
444
152
592
174
560
449
156
600
180
570
453
161
608
186
580
457
165
616
192
590
461
170
624
198
600
464
174
632
205
610
468
179
640
211
123
Uom /kJ mol-1
Thermodynamic investigation of Rb2FeTi(PO4)3 phosphate of langbeinite structure Table 4 continued
Hmo ðTÞ Hmo ð6Þ /kJ mol-1
Som ðTÞ Som ð6Þ /J mol-1 K-1
T/K
o Cp;m /J mol-1 K-1
Uom /kJ mol-1
620
471
184
647
217
630
473
189
655
224
640
476
193
662
230
650
478
198
670
237
Standard for temperature u(T) = 0.01 K in the temperature range from T = 5–345 K and u(T) = 0.5 K in the interval between T = 330 and 650 K. The standard uncertainty for pressure u(p) = 10 kPa. Combined expanded uncertainties for the heat capacity Uc(Cop,m) are 0.02, 0.005, 0.002 and 0.02; the combined expanded uncertainties Uc[H(T) - H(6)] are 0.022, 0.007, 0.005 and 0.022; Uc[S(T) - S(6)] are 0.023, 0.008, 0.006 and 0.023; Uc[Uom] are 0.03, 0.01, 0.009 and 0.03 in the ranges 6 B T/K B 15, 15 B T/K B 40, 40 B T/K B 345 and 330 B T/K B 650, respectively, for 0.95 level of confidence (k & 2)
Conclusions • •
•
•
The heat capacity of crystalline Rb2FeTi(PO4)3 was measured in the range from 6 to 650 K. The heat capacity curve showed the anomaly, which is likely to be descending branch for magnetic disorder– order phase transition, lying at T below 6 K. Using low-temperature heat capacity data, the structural topology of Rb2FeTi(PO4)3 was established as a three-dimensional (framework). From experimental data, the standard thermodynamic functions of Rb2FeTi(PO4)3, namely the heat capacities o o , enthalpies Hm ðTÞ Hmo ð6Þ , entropies Cp;m o o o Sm ðTÞ Sm ð6Þ and Gibbs energies Um within the range T ? 6–650 K, were calculated.
Acknowledgements The present work was performed at the Lobachevsky State University of Nizhni Novgorod with the financial support of the Russian Foundation for Basic Research (Project No. 15-03-00716) based on equipment of Common Use Center «New materials and resource-recovery technologies» (Agreement N 14.594.21.0005).
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